The policy rule in the previous section puts weight on both the deviation of the output and the inflation, together with the policy smoothing parameters (rtn= 0.9rtn−1+ 1.5πt+ 0.5yt). In
this section, the simple Taylor’s rule is applied. The policy smoothing parameter is removed and will only focus on the deviation of the inflation from the steady state value (a version of the inflation targeting policy)rnt = 1.5πt. The same experiments as in the previous section are
conducted. Similar to the results in the previous section, the major source of the asymmetry is the nonlinear Phillips curve while the financial accelerator magnifies the effects. The asym- metric effects of the monetary policy are most prominent in M odel4 in which both channels are operating. Thus, this section will only discuss the results fromM odel4.
The degree of asymmetry in the previous section decreases when the simple Taylor’s rule is applied. There is barely asymmetric effects found in Figure 3.13. There are two changes in policy rules from the previous section: the AR parameter and the weight on the deviation of output are dropped. Putting less weight on the deviation of the output and the inflation intensifies the degree of asymmetry (the results are not shown here). By dropping theses two
parameters, the asymmetry is expected to diminish. Instead, the less degree of asymmetry is observed, indicating an important role of the smoothing parameter in explaining the asym- metry. The policy’s smoothing parameter and price stickiness work in similar manner. The more the degree of price stickiness increases, the more effective the monetary policy becomes. Without the smoothing parameter, the nominal interest rate promptly responds to the changes in the economy.
The effects of a convex supply curve can be observed in Figure 3.14 and Figure 3.15, albeit with smaller magnitudes. The output responds less to policy shocks at expansions than at recessions when demand shocks hit the economy, while other price-related variables respond more. On the other hand, when supply shocks hit the economy, the output is more sensitive to policy shocks during expansions, while other price-related variables become less sensitive to the policy shocks.
The last experiment investigates the role of size of the shocks (the results are not included). The degrees of the asymmetry found in the previous section are sensitive to the size of the shocks. The size of the shocks used in the previous section are ±1 and ±2 of the standard deviation of monetary policy shocks, which is equal to 0.0034. A higher standard deviation generates more asymmetry. This test suggests that the size of shocks is important. Theoret- ically, the model and its nonlinearity can produce the asymmetric responses associated with a certain set of parameters and the size of the shocks. However, the size of the policy shocks beyond 2 standard deviation seem to be unrealistic. Thus, it is possible that the theoretical mechanisms are not able to explain the asymmetry or the solution method fails to preserve enough nonlinearity of the model, or both.
3.6
Conclusion
It has been observed for many decades that while monetary policy is an effective tool to slow down a heating economy, it seems to fail to fight a recession. Milton Friedman compares these asymmetric effects of monetary policy to pushing a string: “you can keep pushing the string
but nothing will happen”. With the evidences of the asymmetry at the peaks of business cycle, researchers have attempted to investigate the asymmetry in other positions of business cycle and explored the study to other definitions of the asymmetry. In addition, attempts to explain the causes and the mechanisms by which the asymmetry is created have also been made. Although the results are mixed, empirical works have documented the asymmetric effects of monetary policy in many countries and many aspects. Those works are supported by three groups of theories: the convex supply curve, the financial friction and the economic outlook.
The linkage between the empirical and theoretical works is important. For empirical works, nonlinear econometrics is applied to capture the asymmetry. Traditionally, the estimable equations are linked to the theoretical models via a reduced-form model. Thus, the estimates cannot be fully linked to the parameters that govern the asymmetry. Consequently, although the theories seem to be able to explain the mechanism by which the asymmetry is created quite well, the extents to which they contribute to the asymmetry are unknown. As for the theoretical works, some potential models such as the menu cost, are constructed in a partial equilibrium framework. With a partial equilibrium framework, the analytical solutions can be obtained and tested. However, a conclusion of the model might be different when other parts of the economy are considered, as in a general equilibrium framework. A model in this framework itself is a highly nonlinear system. Due to its complexity, the analytical solutions cannot be obtained. Traditionally, the model will be linearized or log-linearized to find the solutions. However, by doing so, the nonlinearity of the model is canceled out. Therefore, the model is no longer capable of explaining asymmetric effects of the policy.
This paper applies the second-order perturbation method to find the solutions of the model and to preserve the nonlinearity. Two out of three groups of theories explaining the causes of the asymmetry are considered: the convex supple curve and the financial friction. The nonlinear Phillips curve, driven by Calvo pricing, is applied to create a convex supply and Bernanke et al. (1998)’s financial accelerator model is devised to produce financial friction. The model parameters are calibrated to the U.S. economy. Three types of asymmetric effects monetary policy shocks are tested: the difference between 1) expansionary and contractionary
policies, 2) moderate and aggressive policies, and 3) policies implemented at expansions and recessions.
Even though the degree of the asymmetry is reduced when a simple Taylor’s rule is ap- plied, the asymmetric effects of the monetary policy are found when a standard policy rule is used. Between the two sources of the asymmetry, the financial friction amplifies the effects of monetary policy but does not explain the asymmetric responses. The source of asymmetry mostly comes from the nonlinear Phillips curve through a convex supply curve. The trading off between the output growth and the inflation drives the system to respond nonlinearly to policy shocks. As a result, expansionary policies are found to have greater effects on the price but smaller effects on the output. In contrast, the asymmetry between moderate and aggres- sive policies is not found. When compare the effects of the policies implemented at expansions and recessions, the direction of the asymmetry depends on the type of shocks that drive the business cycle. While both positive demand and supply shocks increase the output level, the demand shocks put more pressure on the prices while supply shock deflates the prices. With a lower (higher) price level, the monetary policy shocks can have higher (lower) effects on the output with less (more) effects on the price. Thus, monetary policy shocks have stronger effects on the output and weaker effects on the price, when the demand shocks drive the business cycle. The degree of the asymmetry also depends on the parameters of the policy rule. The degree of asymmetry increases when the policy puts less weight on the deviation of the output and the inflation, and when the smoothing parameter is higher.